Pre-distortion using a by-pass signal

ABSTRACT

An output signal from an inherently non-linear device is linearized by sampling an original signal with a first sampling rate for a desired signal resolution of an achieved digital original signal message; and re-sampling the original signal at a second sampling rate for creating a digital pre-distortion signal to be added to the achieved digital original signal message. The second sampling rate is greater than the first sampling rate, thereby forming a digital pre-distorted signal to be fed to the inherently non-linear device after digital to analog conversion.

This application is the US national phase of international applicationPCT/SE02/01074, filed in English on 05 May 2002, which designated theUS. PCT/SE02/01074 claims priority to SE Application No. 0102122.9 filed14 Jun. 2001. The entire contents of these applications are incorporatedherein by reference.

BACKGROUND

I. Field of the Invention

This invention relates to digital pre-distortion of an inherentlynon-linear device. Specifically it deals with achieving a broadbanddigital signal with high resolution as a pre-distorted signal withoutthe need for fast D/A converters using a high number of bits for highresolution.

II. Related Art and Other Considerations

One of the operator's main goals is to be able to offer high capacity totheir customers in the network. High capacity in terms of number ofchannels in a cellular network requires in turn a tightening of thefrequency plan. That is, more frequencies must be made available in agiven area than before. The base station has to handle more carriers atthe same site. Conventional systems like TDMA (DAMPS) and GSM requiremore channels and upcoming systems like the WCDMA instead requires acontinuous wide bandwidth. This in turn calls for ultra linearamplifiers.

Linear amplifiers are used to amplify several carriers at the same time,as opposite to amplifying each carrier separately and then add them upin, for example, a hybrid-combiner. Hybrid-combiners such as 90° branchline couplers have the disadvantage that for each doublet of carriersthere is a 3 dB power loss.

A linear power amplifier typically has an efficiency of about 6% but itkeeps relatively constant efficiency as more carriers are added.Moreover, only one amplifier has to be used for all carriers. The mainproblem with power amplifiers is the linearity of the AM-AMcharacteristics, whereas hybrid combiners do not suffer from this. Mostcellular systems require inter-modulation (IM) products to be in theorder of 70 dB down from the carrier. Extensive work has been done tolinearize power amplifiers of which feed-forward seems to be the mostpromising method. Inter-modulation products are simply subtracted at theoutput of the amplifier by comparing input and output signals of themain amplifier. An error-amplifier adjusts the level of theinter-modulation frequency products (output minus input).

Feed-forward can improve linearity to a certain degree but then itbecomes very difficult to achieve the last few dB's necessary for fullcompliance. A way of further linearizing the amplifier is to pre-distortthe input signal to the amplifier and compensate for the non-linearity.There are a number of ways as how to accomplish this. One way is topre-distort within the feed-forward loop of the MCPA itself. Usuallythis is done in an analog RF fashion. RF pre-distortion (PD) may also bedone outside the full MCPA.

Another way is to implement digital pre-distortion. Digital PD may beused whenever there is a digital combined signal at hand. Theintroduction of so-called software transceivers makes it particularlyconvenient to extract this signal. On a system-level there would be adigital software transceiver, a broadband digital-to-analog converter(DAC), some RF components and the RF MCPA basically connected to theantenna port. A digital pre-distorter would preferably be placed betweenthe software transceiver and the DAC.

There is a need for pre-distortion as a means for or complementingclassical linearization techniques for non-linear devices. Such devicesmay be single-carrier power amplifiers (SCPA) or for examplemulti-carrier power amplifiers (MCPA), or even passive devices.

Linearization, as it is usually implemented for broadband applications,is to use feed forward techniques. By using this technique it ispossible to subtract unwanted signal components by comparing the signalbefore and after the non-linear device. Linearization can beaccomplished to a certain degree but is normally implemented in analogfashion with its difficulties, which has to be taken care of,essentially at RF frequencies.

Digital pre-distortion, on the other hand, is usually accomplished atbase-band or at some intermediate frequency (IF). Essentially the ideais to perform this where the best control of the signal is achieved, andalso where the carrier frequency is much lower than at a real operatingfrequency.

Designers have been working with linearization basically from the pointwhen amplification of electric signals started off. As a description ofthe State-of-the-art in linearization techniques one way is to implementpre-distortion in an analog fashion at analog RF directly in front ofthe non-linear device. Alternatively it may be incorporated within thefeed-forward loop in the MCPA itself (if that is the non-linear device).Some ideas have been put forward to place the pre-distorter also atdigital base-band as indicated in FIG. 7. The digital signal is copiedand fed through a digital pre-distorter and then added to the originaldigital signal again before it is fed to the D/A converter. Thecorrection is made completely to the digital signal.

For instance, in U.S. Pat. No. 5,598,436 is described a digitaltransmission system with pre-distortion. However, the circuitry usesdifferent quantification levels for the phase and the amplitude,respectively.

Another U.S. Pat. No. 6,172,562 describes a pre-distorter forcontrolling the phase and amplitude in order to linearize a non-lineardevice. The document discusses the problem with high bandwidth demandswhen using high accuracy digital circuits. Separating the phase andamplitude corrections into two parallel branches then solves thisproblem.

In an article in Electronics Letters Vol. 33 Nov. 11, 1997 titled “Chipfor wide-band digital pre-distortion RF power amplifier linearization” acustom chip for digital pre-distortion is disclosed in which the forwardpath and the adaptation/control path work with different speeds at astandard resolution of 14 bits. It is pointed out that the linearizerhas to operate with a sampling frequency typically four to eight timeshigher than the signal bandwidth.

Thus, the drawback of today's solution is that a fairly large bandwidthhas to be associated with the distorted signal. As most non-lineardevices can be modeled as a power series (see FIG. 2), it is clear thatsignal components whose frequencies are linear combinations of theoriginal ones will appear in the output signal. For example, if the mainnon-linearity is a x³-component, there will occur frequencies thatoccupy 3 times as large bandwidth as the original signal (FIG. 1 andFIG. 2). And likewise there will occur frequencies from non-linearitythat have also an x⁵-component, which will give rise to actually 5 timesas large bandwidth. The same argumentation can be used for furtherhigher components.

As can be concluded from the above discussion, it is necessary to feed asignal into the device which in itself has the same required bandwidthas the distorted signal wanted to be improved. As there practically is arelation existing between the dynamic range (number of bits, orresolution) for a D/A converter and the sampling frequency, it is alsoclear that achieving a higher bandwidth of the pre-distorted signal alsorequires better D/A converters. A low resolution D/A converter mayoperate at a very high sampling rate, but oppositely it is difficult todesign a high resolution D/A converter at the same high sampling rate.

Another view to the problem is that aliases (periodic copies) in thespectrum may occur if one is using a too low sampling rate. So, adding apre-distorted signal to the original one will cause overlapping signalspectrum as indicated in FIG. 6. The original (analog) signal can nolonger be uniquely filtered out properly without suffering from aliasingeffects. Performing a D/A-conversion means essentially that the originalspectrum in FIG. 3 should be possible to filter out in the digitalrepresentation as seen in FIG. 4. If the sampling rate from the start istoo low in comparison to the signal bandwidth, aliasing effects as shownin FIG. 5 will occur.

BRIEF SUMMARY

Different D/A converters are used for two signals, i.e. for the originaldigital message signal (A-branch in FIG. 8) and the pre-distorteddigital signal part (B-branch in FIG. 8). In other words, the same highresolution and moderate sampling frequency D/A converter is used for theoriginal digital message signal as is used conventionally, but a D/Awith lower resolution with higher sampling rate is used for the addedpre-distortion signal. The two signals are then combined in their analogdomain. Thus, requirements on high sampling rates for both signals atthe same time are avoided. Care should of course be taken to ensure thatthe two added signals have the proper time alignment or phase alignment.

The distorted contribution to the signal only has signal components thatare in the order of the distortion level that are to be subtracted. Forexample, if the distortion in terms of harmonics is 50 dB below thecarrier level on the output of the non-linear device, we only have tosee what resolution we must have to come down to the level we desire. Ifthe desired level is 80 dB below the carrier level, then it is clearthat a dynamic range is needed which is equivalent to (80−50=)30 dB. Interms of number of bits in a D/A converter this equals 30/6=5 bitresolution where 6 dB [20 log(2)] accounts for every additional bit.

SHORT DESCRIPTION OF THE DRAWINGS

The invention, together with further objects and advantages thereof, maybest be understood by making reference to the following descriptiontaken together with the accompanying drawings, in which:

FIG. 1 is an example of input spectrum wherein the bandwidth is B andthe amplification is constant, that is G(v)=G₀·v;

FIG. 2 is an example of an input spectrum together with distortedcomponents as measured at the output of a 3^(rd) order non-linearity,whereby the bandwidth of the distortion is 3 times larger than theoriginal input spectrum of the signal;

FIG. 3 is an example of an analog input spectrum represented by itsnegative as well as positive frequency portions, whereby the low andhigh frequency end points f_(L) and f_(H) respectively indicate thebandwidth;

FIG. 4 illustrates the analog signal of FIG. 3 sampled at a samplingrate f_(S) and the spectrum is repeated periodically with distancef_(S), whereby the sampling process is repeating both negative andpositive frequency parts;

FIG. 5 illustrates sampling of a signal with too low sampling rate,whereby the alias effect will destroy the possibility to reconstruct theoriginal analog signal by filtering;

FIG. 6 illustrates that if sampling rate is too low, the needed extrabandwidth for the pre-distorted signal part will overlap other duplicatespectra and it is not possible to recover the 3 times (or more) largerbandwidth signal that is needed for pre-distortion;

FIG. 7 illustrates conventional digital pre-distortion wherein a portionof the original signal is pre-distorted and again re-inserted into thesignal, which is D/A converted before being fed to the non-lineardevice, the drawback of the solution being the inherent lack ofbandwidth of the D/A converter (at the specific sampling rate anddynamic range);

FIG. 8 illustrates an example of pre-distortion by use of the proposednew method of bypassing to a separate D/A converter with a lowerresolution, whereby this D/A converter can run at a much higher samplingrate with respect to manufacturing standard of today;

FIG. 9 a shows output spectrum from the MCPA without pre-distortion foran example when a 4-tone carrier ensemble is fed through a nonlineardevice;

FIG. 9 b shows output spectrum for MCPA when the carriers themselveshave been suppressed to highlight the distortion itself;

FIG. 10 a shows a signal spectrum of four equal CW carriers at regularfrequency intervals fed through a nonlinear pre-distortion devicecharacterized by Equation (2) and fed to the non-linear MCPA asdescribed by Equation (3), whereby the pre-distortion part has beencomputed at a resolution of 3 bits and carriers part at resolution of 15bits;

FIG. 10 b shows a corresponding diagram as FIG. 10 a except that a fullresolution of 15 bits is used for both signal parts;

FIG. 11 a shows the same spectrum as in FIG. 10 a where the carriershave been subtracted to highlight the distorted spectrum part;

FIG. 11 b shows the same spectrum as in FIG. 10 b where the carriershave been subtracted to highlight the distorted spectrum part;

FIG. 12 a shows a signal spectrum of four equal CW carriers at regularfrequency intervals fed through a nonlinear pre-distortion devicecharacterized by Equation (2) and fed to the non-linear MCPA asdescribed by Equation (3), whereby the pre-distortion part has beencomputed at a resolution of 7 bits;

FIG. 12 b shows a corresponding spectrum as 12 a but with fullresolution of 15 bits are used for both signal parts, illustrating analmost negligible difference compared to FIG. 12 a;

FIG. 13 a shows the same spectrum as in FIG. 12 a except for the carrierparts, which have been subtracted to highlight the distorted spectrum;and

FIG. 13 b shows the same spectrum as in FIG. 12 b except for the carrierparts, which have been subtracted to highlight the distorted spectrum.

DETAILED DESCRIPTION

Below will be discussed a method for achieving a broadband signal withhigh resolution as a pre-distorted signal without the need for D/Aconverters that have these properties in the same device. The discussionwill utilize spectra for illustrating example embodiments and modes.

Different D/A converters are used for two signals, i.e. for the originaldigital message signal (A-branch in FIG. 8) and the pre-distorteddigital signal part (B-branch in FIG. 8). In other words, the same highresolution and moderate sampling frequency D/A converter is used for theoriginal digital message signal as is used conventionally, but a D/Awith lower resolution with higher sampling rate is used for the addedpre-distortion signal. The two signals are then combined in their analogdomain. Thus, requirements on high sampling rates for both signals atthe same time are avoided. Care should of course be taken to ensure thatthe two added signals have the proper time alignment or phase alignment.

The distorted contribution to the signal only has signal components thatare in the order of the distortion level that are to be subtracted. Forexample, if the distortion in terms of harmonics is 50 dB below thecarrier level on the output of the non-linear device, we only have tosee what resolution we must have to comedown to the level we desire. Ifthe desired level is 80 dB below the carrier level , then it is clearthat a dynamic range is needed which is equivalent to (80−50=)30 dB. Interms of number of bits in a D/A converted this equals 30/6=5 bitresolution where 6 dB [20 log(2)] accounts for every additional bit.

Assume that we have a signal that is a 4-tone continuous wave (CW)signal as described by Equation (1) below. This signal shall be fedthrough a non-linear device such as for example an MCPA with thenon-linear characteristics as described by Equation 3. This equationdescribes a polynomial approximation to the non-linear function and canalso be extended to include the phase variation as a function ofamplitude. In order to counter-act the non-linear behavior of thisdevice a pre-distorter is designed to minimize the distortion orinter-modulation products in the output of the device. Thispre-distorter is found to be as described in Equation (3) below.Derivation of this particular function and its coefficients is notconsidered crucial for understanding of the technology but provides agood example.

Signal:a(t):=sin(2·πf1·t)+sin(2·π·f2·t)+sin(2·π·f3·t)+sin(2·πf4·t)  (1)Distorted signal:α:=0.005g(t):=a(t)·1+α·a(t)³  (2)Pre-distortion signal sent through a MPCAβ:=−0.00005MPCA(t)=g(t)−α·g(t)³ −β·g(t)⁵  (3)

If the signal in Equation (1) is fed into the non-linear device asexemplified by the MCPA characteristics in Equation (3), we will get adistorted signal spectrum which is depicted in FIG. 9 a and FIG. 9 b. Itshould be noted that we have not yet applied the pre-distortion. So wesee that for this particular choice of non-linear function we have adistortion level (or inter-modulation level if you like) that is in thiscase only some 30 dB's below the carrier level.

FIG. 12 a and FIG. 12 b shows the output spectrum of the combinedpre-distorter and non-linear device (e.g. MCPA). The two graphs show thecomparison between using full resolution (number of bits) to using onlyfor example 7 bits for the B-branch, which is the by-passed part. As canbe seen there is almost no visible difference between the two curves. Byextracting the carrier part it is even more evident by view of FIG. 13 aand FIG. 13 b. The two graphs show the same signal spectrums as in theprevious graph, only the carriers have been taken out and only thedistortion is left. It is seen that the inter-modulation for thisparticular choice of coefficients has been improved by around 30 dB.

As a further example, we may reduce the number of bits in the resolutionto only 3 bits (including the sign bit). The result is shown in FIG. 10a and FIG. 12 b together with the same output if we would have fullresolution of 15 bits in both A- and B-branches. Now there is a morenoticeable difference but still, in view of FIG. 11 a and FIG. 11 bwhere the carriers have been removed, the level ofdistortion/inter-modulation is reduced by 30 dB. The only difference inthis case is that a broad band of spurious signals can be seen that wasnot there in the previous example with 7 bit resolution.

The simulated results described herein show that use of two separate D/Aconverters for the A- and B-branches gives very good results in terms ofintermodulation levels.

Thus, the technology described herein encompasses a method, by means ofdigital pre-distortion, of linearizing an output signal from aninherently non-linear device producing intermodulation or non-linearproducts in its output signal. In an example embodiment, the methodcomprises the acts of:

sampling an original signal with a high number of bits at a givensampling rate for a desired signal resolution of an achieved digitaloriginal signal message; and

re-sampling the original signal at a lower number of bits with a severaltimes higher sampling rate for creating a digital pre-distortion signalto be added to the achieved digital original signal message, therebyforming a digital pre-distorted signal to be fed to the inherentlynon-linear device after digital to analog conversion.

In further aspects, the method can comprise the acts of:

using, for a first high resolution digital signal, a sampling frequencycorresponding to at least twice the highest frequency of a desiredoriginal signal message bandwidth in accordance to the Nyquist theorem;

using, for a second digital signal, a high sampling rate correspondingto a frequency of at least a desired B-branch error message bandwidth,and

whereby a resolution in bits of the original digital message is definedby a desired dynamic range below a carrier in decibels level beingA_(DB), and the resolution in number of bits of the pre-distorteddigital signal to be added is defined as at least (A_(DB)−B_(DB))/6,wherein B_(DB) is level of harmonics below the carrier in decibels to becancelled.

In further aspects, the method can comprise the acts of:

selecting for the first high resolutions digital signal A/D conversionof 16 bits, and

selecting for the second low resolution digital signal A/D conversion of8 bits with, e.g., three times the sampling frequency of the first highresolution digital signal.

In further aspects, the method can comprise the acts of:

selecting for the first high resolutions digital signal A/D conversionof 16 bits, and

selecting for the second low resolution digital signal A/D conversion of6 bits at an even higher sampling e.g. with five times the samplingfrequency of the first high resolution digital signal.

Advantageously, no change in sampling rate needs to be implemented inthe original signal in order to provide a wide-band pre-distortedsignal. A wide-band signal for the pre-distortion part is required topre-distort a signal on the input of a non-linear device such as forexample an MCPA. However, since this broadband signal is added after D/Aconversion in the analog signal domain, there is no restriction on thesampling rate of the original signal. Only the by-passed distortion partof the signal has to be implemented with a high sampling rate. A realbenefit from this proposal is that this by-pass D/A converter need notbe a high resolution D/A, but can be any ordinary low cost D/A but withhigh sampling rate. Thus, digital pre-distortion can be implementedusing existing D/A converters without loss of performance when connectedto the non-linear device such as the MCPA.

Linearizing an output signal from an inherently non-linear deviceproducing intermodulation products in its output signal as a response toan input signal, in accordance with the present invention, may beembodied in a numerous number of ways without departure from the scopeand spirit of the present invention, which is defined by the attachedclaims.

1. A method, by means of digital pre-distortion, of linearizing anoutput signal from an inherently non-linear device producingintermodulation or non-linear products in its output signal, the methodcomprising: sampling an original signal with a first sampling rate for adesired signal resolution of an achieved digital original signalmessage; re-sampling the original signal at a second sampling rate forcreating a digital pre-distortion signal, the second sampling rate beinggreater than the first sampling rate; performing a digital to analogconversion of the digital sample original signal to obtain ananalog-converted original signal and performing a digital to analogconversion of the digital pre-distortion signal to obtain ananalog-converted pre-distortion signal; adding the analog-convertedoriginal signal and the analog-converted pre-distortion signa1, therebyforming a pre-distorted signal to be fed to the inherently non-lineardevice.
 2. The method according to claim 1, further comprising: usingfor a first high resolution digital signal a sampling frequencycorresponding to at least twice the highest frequency of a desiredoriginal signal message bandwidth in accordance to the Nyquist theorem;using for a second digital signal a high sampling rate corresponding toa frequency of at least a desired error message bandwidth, whereby aresolution in bits of the original digital message is defined by adesired dynamic range below a carrier in decibels level being A_(DB),and the resolution in number of bits of the pre-distortion digitalsignal to be added is defined as at least (A_(DB)−B_(DB))/6, whereinB_(DB) is the level of harmonics below the carrier in decibels to becancelled.
 3. The method according to claim 2, further comprising:selecting, for the first high resolution digital signal, resolution of16 bits, and selecting, for the second digital signal, a resolution of 8bits at three times the sampling frequency of the first high resolutiondigital signal.
 4. The method according to claim 2, further comprising:selecting, for the first high resolution digital signal, a resolution of16 bits, and selecting, for the second digital signal, a resolution of 6bits five times the sampling frequency of the first high resolutiondigital signal.
 5. A digital pre-distorter configured to receive anoutput signal from an inherently non-linear device, the non-lineardevice producing intermodulation or non-linear products in its deviceoutput signal, the circuitry comprising: a first branch comprising afirst digital to analog converter and configured to receive the deviceoutput signal, the first digital to analog converter being configured tosample the device output signal at a first sampling rate and at a firstresolution and to provide first analog signal; a second branchcomprising a second digital to analog converter configured to receive apredistortion signal based on a resampling of the device output signal,the second analog to digital converter being configured to sample thepre-distortion signal at a second sampling rate and at a secondresolution and to provide a second analog signal; wherein the secondsampling rate is higher than the first sampling rate; wherein the secondresolution is lower than the first resolution; and a combiner configuredto combine, in an analog domain, the first analog signal and the secondanalog signal for forming a pre-distorted signal.
 6. The apparatus ofclaim 5, wherein the first resolution is sixteen bits and the secondresolution is 8 bits.
 7. The apparatus of claim 6, wherein the firstsecond sampling rate is three times the first sampling rate.
 8. Theapparatus of claim 5, wherein the first resolution is sixteen bits andthe second resolution is six bits.
 9. The apparatus of claim 8, whereinthe first second sampling rate is five times the first sampling rate.10. The apparatus of claim 5, wherein a resolution in bits of the deviceoutput signal is defined by a desired dynamic range below a carrier indecibels level being A_(DB), and the resolution in number of bits of thepre-distortion signal to be added is defined as at least(A_(DB)−B_(DB))/6, wherein B_(DB) is the level of harmonics below thecarrier in decibels to be cancelled.
 11. A method of performing digitalpre-distortion of an output signal received from an inherentlynon-linear device, the non-linear device producing intermodulation ornon-linear products in its device output signal, the method comprising:using a first digital to analog converter to sample the device outputsignal at a first sampling rate and at a first resolution and to providea first analog signal; using a second analog to digital converter tosample a pre-distortion signal at a second sampling rate and at a secondresolution and to provide a second analog signal; wherein the secondsampling rate is higher than the first sampling rate; wherein the secondresolution is lower than the first resolution; and combining, in ananalog domain, the first analog signal and the second analog signal. 12.The method of claim 11, wherein the first resolution is sixteen bits andthe second resolution is 8 bits.
 13. The method of claim 12, wherein thefirst second sampling rate is three times higher than the first samplingrate.
 14. The method of claim 11, wherein the first resolution issixteen bits and the second resolution is six bits.
 15. The method ofclaim 14, wherein the first second sampling rate is five times the firstsampling rate.
 16. The method of claim 11, wherein a resolution in bitsof the device output signal is defined by a desired dynamic range belowa carrier in decibels level being A_(DB), and the resolution in numberof bits of the pre-distortion signal to be added is defined as at least(A_(DB)−B_(DB))/6, wherein B_(DB) is the level of harmonics below thecarrier in decibels to be cancelled.
 17. The method of claim 11, furthercomprising providing alignment of the first analog signal and the secondanalog signal prior to combining the first analog signal and the secondanalog signal.